Tides on the Moon: Theory and determination of dissipation

The aim of this work is to combine the model of orbital and rotational motion of the Moon developed for DE430 with up-to-date astronomical, geodynamical, and geo-and selenophysical models. The parameters of the orbit and physical libration are determined in this work from lunar laser ranging (LLR) observations made at different observatories in 1970-2013. Parameters of other models are taken from solutions that were obtained independently from LLR.A new implementation of the DE430 lunar model, including the liquid core equations, was done within the EPM ephemeris. The postfit residuals of LLR observations make evident that the terrestrial models and solutions recommended by the IERS Conventions are compatible with the lunar theory. That includes: EGM2008 gravitational potential with conventional corrections and variations from solid and ocean tides; displacement of stations due to solid and ocean loading tides; and precession-nutation model. Usage of these models in the solution for LLR observations has allowed us to reduce the number of parameters to be fit. The fixed model of tidal variations of the geopotential has resulted in a lesser value of Moon's extra eccentricity rate, as compared to the original DE430 model with two fit parameters.A mixed model of lunar gravitational potential was used, with some coefficients determined from LLR observations, and other taken from the GL660b solution obtained from the GRAIL spacecraft mission.Solutions obtain accurate positions for the ranging stations and the five retroreflectors. Station motion is derived for sites with long data spans. Dissipation is detected at the lunar fluid core-solid mantle boundary demonstrating that a fluid

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“…A simple model of solid Moon tides was used in this work, while more detailed models have been recently developed; see (Williams and Boggs 2015).…”

Section: Reductions Of Observationsmentioning

confidence: 99%

Determining parameters of Moon’s orbital and rotational motion from LLR observations using GRAIL and IERS-recommended models

Pavlov

Williams

Suvorkin

2016

Celest Mech Dyn Astr

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“…The CMB flattening, ε f , is poorly constrained by lunar laser ranging observations [e.g., Williams and Boggs , ], but it is probable that it is also in a state of hydrostatic equilibrium given the high temperatures deep in the Moon. Assuming hydrostatic equilibrium, and adapting the methodology presented in Veasey and Dumberry [], ε f can be expressed in terms of ε r , ε m and ε s ,

ε_{f} = k_{fr} ε_{r} + k_{fm} ε_{m} + k_{fs} ε_{s},

where

k_{fr} = \frac{ρ_{c}}{scriptP}, k_{fm} = \frac{ρ_{m} - ρ_{c}}{scriptP}, k_{fs} = \frac{{((), \frac{r_{s}}{r_{f}})}^{5} ((), ρ_{s} - ρ_{f})}{scriptP},

scriptP = ρ_{m} + \frac{2}{3} ρ_{f} + \frac{5}{3} {((), \frac{r_{s}}{r_{f}})}^{3} ((), ρ_{s} - ρ_{f}) .

…”

Section: Theorymentioning

confidence: 99%

The forced precession of the Moon's inner core

Dumberry

Wieczorek

2016

JGR Planets

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The tilt angle of the 18.6 year precession of the Moon's solid inner core is unknown, but it is set by a balance between gravitational and pressure torques acting on its elliptical figure. We show here that to first order, the angle of precession of the inner core of a planetary body is determined by the frequency of the free inner core nutation, ωficn, relative to the precession frequency, Ωp. If |ωficn|≪|Ωp|, the inner core is blind to the gravitational influence of the mantle. If |ωficn|≫|Ωp|, the inner core is gravitationally locked to the mantle and is nearly aligned with it. If ωficn≈Ωp, large inner core tilt angles can result from resonant excitation. Viscous inner core relaxation and electromagnetic coupling can attenuate large tilt angles. For the specific case of the Moon, we show that ωficn is to within a factor of 2 of Ωp = 2π/18.6 yr−1. For a rigid inner core, this implies a tilt of 2 to 5° with respect to the mantle, and larger if ωficn is very close to Ωp. More modest tilt angles between 0 and 0.5° result if viscous relaxation within the inner core occurs on a timescale of one lunar day. Predictions from our model may be used in an attempt to detect the gravity signal resulting from a tilted inner core, to determine the past history of the inner core tilt angle, and to assess models of dynamo generation powered by differential rotation at the core‐mantle and inner core boundaries.

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“…Even assuming a lower than current tidal quality factor Q = 100 for the Moon during the in the interior at the time of the transition, its Love number would be higher than it is now, again leading to more rapid inclination damping. Third, we assumed constant tidal properties for Earth throughout the calculation, which is in conflict with the fact that the current rate of the Moon's tidal recession is about three times higher than the long-term average 35 . An increase in the tidal dissipation within Earth's oceans over time as suggested by modeling 36,37 would mean that the Moon spent more time at the Cassini state transition than we calculated, allowing more damping of inclination.…”

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confidence: 99%

Tidal evolution of the Moon from a high-obliquity, high-angular-momentum Earth

Ćuk

Hamilton

Lock

et al. 2016

Nature

131

103

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In the giant impact hypothesis for lunar origin, the Moon accreted from an equatorial circumterrestrial disk; however the current lunar orbital inclination of 5 • requires a subsequent dynamical process that is still debated [1][2][3] . In addition, the giant impact theory has been challenged by the Moon's unexpectedly Earth-like isotopic composition 4, 5 . Here, we show that tidal dissipation due to lunar obliquity was an important effect during the Moon's tidal evolution, and the past lunar inclination must have been very large, defying theoretical explanations. We present a new tidal evolution model starting with the Moon in an equatorial orbit around an initially fast-spinning, high-obliquity Earth, which is a probable outcome of giant impacts. Using numerical modeling, we show that the solar perturbations on the Moon's orbit naturally induce a large lunar inclination and remove angular momentum from the 1 arXiv:1802.03356v1 [astro-ph.EP] 9 Feb 2018Earth-Moon system. Our tidal evolution model supports recent high-angular momentum giant impact scenarios to explain the Moon's isotopic composition [6][7][8] and provides a new pathway to reach Earth's climatically favorable low obliquity.The leading theory for lunar origin is the giant impact 9, 10 , which explains the Moon's large relative size and small iron core. Here we refer to the giant impact theory in which the Earth-Moon post-impact angular momentum (AM) was the same as it is now (in agreement with classic lunar tidal evolution studies 11, 12 ) as "canonical". In the canonical giant impact model 13 , a Mars-mass body obliquely impacts the proto-Earth near the escape velocity to generate a circum-terrestrial debris disk. The angular momentum of the system is set by the impact, and the Moon accretes from the disk, which is predominantly (> 60 wt%) composed of impactor material. However, Earth and the Moon share nearly identical isotope ratios for a wide range of elements, and this isotopic signature is distinct from all other extraterrestrial materials 4, 5 . Because isotopic variations arise from multiple processes 4 , the Moon must have formed from, or equilibrated with, Earth's mantle 5,14 . Earth-Moon isotopic equilibration in the canonical model has been proposed by Pahlevan and Stevenson 15 , but has been questioned by other researchers 16 , who suggest that the large amount of mass exchange required to homogenize isotopes could lead to the collapse of the proto-lunar disk.Cuk and Stewart 6 proposed a new variant of the giant impact that is based on an initially high AM Earth-Moon system. In this model, a late erosive impact onto a fast-spinning proto-Earth produced a disk that was massive enough to form the Moon, and was composed primarily of material from Earth, potentially satisfying the isotopic observations. Canup 7 presented a variation of a high-2 AM origin in which a slow collision between two similar-mass bodies produces a fast-spinning Earth and disk with Earth-like composition. Subsequently, Lock et al. 8 have argued that a range of hig...

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Tides on the Moon: Theory and determination of dissipation

Cited by 106 publications

References 88 publications

Determining parameters of Moon’s orbital and rotational motion from LLR observations using GRAIL and IERS-recommended models

Determining parameters of Moon’s orbital and rotational motion from LLR observations using GRAIL and IERS-recommended models

The forced precession of the Moon's inner core

Tidal evolution of the Moon from a high-obliquity, high-angular-momentum Earth

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